自旋为1的Babujan-Takhtajan链动力学关联函数的计算
Computation of dynamical correlation functions of the spin-1 Babujan-Takhtajan chain
摘要：
在零温度和零磁场条件下，利用Bethe Ansatz代数方法对自旋为1/2的可积链进行了高自旋推广，数值计算了Babujan-Takhtajan反铁磁自旋为1的链的动力学结构因子.这种方法，它包括在显式的本征态和相关器的莱曼表示的总和的建设，在这里是特别具有挑战性的实施，鉴于存在强烈偏离字符串解决方案的贝特方程。我们表明，这些偏差的仔细处理，使得有可能获得完美的饱和度的总和规则的小系统尺寸，和非常好的饱和度的大系统尺寸的动力学结构因子计算包括所有的两个自旋和四个自旋的贡献。实空间自旋-自旋关联，通过傅立叶变换我们的结果，显示渐近拟合预测从共形场论。
英文摘要：
The dynamical structure factor of the Babujan-Takhtajan antiferromagnetic spin-1 chain is computed numerically at zero temperature and zero magnetic field, using the higher-spin generalization of an Algebraic Bethe Ansatz-based method previously used for spin-1/2 integrable chains. This method, which consists in the explicit construction of eigenstates and the summation of the Lehmann representation of the correlator, is here particularly challenging to implement in view of the presence of strongly deviated string solutions to the Bethe equations. We show that a careful treatment of these deviations makes it possible to obtain perfect saturation of sum rules for small system sizes, and extremely good saturation for large system sizes where the dynamical structure factor is computed by including all two-spinon and four-spinon contributions. The real-space spin-spin correlation, obtained by Fourier transforming our results, displays asymptotics fitting predictions from conformal field theory.
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